Brealey−Meyers: Principles of Corporate Finance, 7th Edition - Chapter 19 pot

Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
CHAPTER NINETEEN
522
FINANCING AND
V A L U A T I O N
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
WE FIRST ADDRESSED problems of capital budgeting in Chapter 2. At that point we said hardly a
word about financing decisions; we proceeded under the simplest possible assumption about fi-
nancing, namely, all-equity financing. We were really assuming an idealized Modigliani–Miller (MM)
world in which all financing decisions are irrelevant. In a strict MM world, firms can analyze real in-
vestments as if they are to be all-equity-financed; the actual financing plan is a mere detail to be
worked out later.
Under MM assumptions, decisions to spend money can be separated from decisions to raise
money. In this chapter we reconsider the capital budgeting decision when investment and financing
decisions interact and cannot be wholly separated.

In the early chapters you learned how to value a capital investment opportunity by a four-step
procedure:
1. Forecast the project’s incremental after-tax cash flow, assuming the project is entirely equity-
financed.
2. Assess the project’s risk.
3. Estimate the opportunity cost of capital, that is, the expected rate of return offered to investors
by the equivalent-risk investments traded in capital markets.
4. Calculate NPV, using the discounted-cash-flow formula.
In effect, we were thinking of each project as a mini-firm, and asking, How much would that mini-firm
be worth if we spun it off as a separate, all-equity-financed enterprise? How much would investors
be willing to pay for shares in the project?
Of course, this procedure rests on the concept of value additivity. In well-functioning capital mar-
kets the market value of the firm is the sum of the present value of all the assets held by the firm
1
—
the whole equals the sum of the parts.
In this chapter we stick with the value-additivity principle but extend it to include value contributed
by financing decisions. There are two ways of doing this:
1. Adjust the discount rate. The adjustment is typically downward, to account for the value of inter-
est tax shields. This is the most common approach. It is usually implemented via the after-tax
weighted-average cost of capital or “WACC.”
2. Adjust the present value. That is, start by estimating the project’s “base-case” value as an all-
equity-financed mini-firm, and then adjust this base-case NPV to account for the project’s impact
on the firm’s capital structure. Thus
Once you identify and value the side effects of financing a project, calculating its APV (adjusted net
present value) is no more than addition or subtraction.
This is a how-to-do-it chapter. In the next section, we explain and derive the after-tax weighted-
average cost of capital, reviewing required assumptions and the too-common mistakes people make
using this formula. Section 19.2 then covers the tricks of the trade: helpful tips on how to estimate
continued

ϩNPV of financing decisions caused by project acceptance
Adjusted NPV 1APV for short2ϭ base-case NPV
523
1
All assets means intangible as well as tangible assets. For example, a going concern is usually worth more than a haphazard pile
of tangible assets. Thus, the aggregate value of a firm’s tangible assets often falls short of its market value. The difference is ac-
counted for by going-concern value or by other intangible assets such as accumulated technical expertise, an experienced sales
force, or valuable growth opportunities.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Think back to Chapter 17 and Modigliani and Miller’s (MM’s) proposition I. MM
showed that, without taxes or financial market imperfections, the cost of capital
does not depend on financing. In other words, the weighted average of the ex-
pected returns to debt and equity investors equals the opportunity cost of capital,
regardless of the debt ratio:
Here r is the opportunity cost of capital, the expected rate of return investors would
demand if the firm had no debt at all; and are the expected rates of return on
debt and equity, the “cost of debt” and “cost of equity.” The weights D/V and E/V
are the fractions of debt and equity, based on market values; V, the total market
value of the firm, is the sum of D and E.
But you can’t look up r, the opportunity cost of capital, in The Wall Street Journal
or find it on the Internet. So financial managers turn the problem around: They
start with the estimates of and and then infer r. Under MM’s assumptions,

This formula calculates r, the opportunity cost of capital, as the expected rate of re-
turn on a portfolio of all the firm’s outstanding securities.
r ϭ r
D

D
V
ϩ r
E

E
V
r
E
r
D
r
E
r
D
ϭ r, a constant, independent of D/V
Weighted-average return to debt and equity ϭ r
D

D
V
ϩ r
E

E

V
524 PART V
Dividend Policy and Capital Structure
inputs and how the formula is used in practice. Section 19.3 shows how to recalculate the weighted-
average cost of capital when capital structure or asset mix changes.
Section 19.4 turns to the Adjusted Present Value or APV method. This is simple enough in con-
cept: Just value the project by discounting at the opportunity cost of capital—not the WACC—
and then add the present values gained or lost due to financing side effects. But identifying and
valuing the side effects is sometimes tricky, so we’ll have to work through some numerical
examples.
Section 19.5 reexamines a basic and apparently simple issue: What should the discount rate be
for a risk-free project? Once we recognize the tax deductibility of debt interest, we will find that
all risk-free, or debt-equivalent, cash flows can be evaluated by discounting at the after-tax inter-
est rate. We show that this rule is consistent with both the weighted-average cost of capital and
with APV.
We conclude the chapter with a question and answer section designed to clarify points that man-
agers and students often find confusing. An Appendix providing more details and more formulas can
be obtained from the Brealey–Myers website.
2
2
www.mhhe.com/bm7e.
19.1 THE AFTER-TAX WEIGHTED-AVERAGE COST
OF CAPITAL
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation

© The McGraw−Hill
Companies, 2003
We have discussed this weighted-average cost of capital formula in Chapters 9
and 17. However, the formula misses a crucial difference between debt and equity:
Interest payments are tax-deductible. Therefore we move on to the after-tax
weighted-average cost of capital, nicknamed WACC:
Here is the marginal corporate tax rate.
Notice that the after-tax WACC is less than the opportunity cost of capital (r), be-
cause the “cost of debt” is calculated after tax as . Thus the tax advantages
of debt financing are reflected in a lower discount rate. Notice too that all the variables
in the weighted-average formula refer to the firm as a whole. As a result, the formula
gives the right discount rate only for projects that are just like the firm undertaking
them. The formula works for the “average” project. It is incorrect for projects that are
safer or riskier than the average of the firm’s existing assets. It is incorrect for projects
whose acceptance would lead to an increase or decrease in the firm’s debt ratio.
Example: Sangria Corporation
Let’s calculate WACC for the Sangria Corporation. Its book and market value bal-
ance sheets are
r
D
11 Ϫ T
c
2
T
c
WACC ϭ r
D
11 Ϫ T
c
2

D
V
ϩ r
E

E
V
CHAPTER 19 Financing and Valuation 525
Sangria Corporation (Book Values, millions)
Asset value $100 $ 50 Debt
50 Equity
$100 $100
Sangria Corporation (Market Values, millions)
Asset value $125 $ 50 Debt (D)
75 Equity (E)
$125 $125 Firm Value (V)
We calculated the market value of equity on Sangria’s balance sheet by multiply-
ing its current stock price ($7.50) by 10 million, the number of its outstanding
shares. The company has done well and future prospects are good, so the stock is
trading above book value ($5.00 per share). However, the book and market values
of Sangria’s debt are in this case equal.
Sangria’s cost of debt (the interest rate on its existing debt and on any new bor-
rowing) is 8 percent. Its cost of equity (the expected rate of return demanded by in-
vestors in Sangria’s stock) is 14.6 percent.
The market value balance sheet shows assets worth $125 million. Of course we
can’t observe this value directly, because the assets themselves are not traded. But
we know what they are worth to debt and equity investors ( mil-
lion). This value is entered on the left of the market value balance sheet.
Why did we show the book balance sheet? Only so you could draw a big X
through it. Do so now.

When estimating the weighted-average cost of capital, you are not interested
in past investments but in current values and expectations for the future. San-
gria’s true debt ratio is not 50 percent, the book ratio, but 40 percent, because its
50 ϩ 75 ϭ $125
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
The company’s WACC is
That’s how you calculate the weighted-average cost of capital.
3
Now let’s see how Sangria would use this formula. Sangria’s enologists have
proposed investing $12.5 million in construction of a perpetual crushing ma-
chine, which, conveniently for us, never depreciates and generates a perpetual
stream of earnings and cash flow of $2.085 million per year pretax. The after-tax
cash flow is
WACC ϭ .0811 Ϫ .352
1.42ϩ .1461.62ϭ .1084, or 10.84%
526 PART V Dividend Policy and Capital Structure
3
In practice it’s pointless to calculate discount rates to four decimal places. We do so here to avoid
confusion from rounding errors. Earnings and cash flows are carried to three decimal places for the
same reason.
Pretax cash flow $2.085
Tax at 35% .730

After-tax cash flow $1.355 million
Notice: This after-tax cash flow takes no account of interest tax shields on debt sup-
ported by the perpetual crusher project. As we explained in Chapter 6, standard
capital budgeting practice calculates after-tax cash flows as if the project were all-
equity-financed. However, the interest tax shields will not be ignored: We are about
to discount the project cash flows by Sangria’s WACC, in which the cost of debt is
entered after tax. The value of interest tax shields is picked up not as higher after-
tax cash flows, but in a lower discount rate.
The crusher generates a perpetual cash flow of million, so NPV is
means a barely acceptable investment. The annual cash flow of $1.355 mil-
lion per year amounts to a 10.84% rate of return on investment ( ),
exactly equal to Sangria’s WACC.
If project , the return to equity investors must exactly equal the cost of
equity, 14.6%. Let’s confirm that Sangria shareholders could actually forecast a
14.6% return on their investment in the perpetual crusher project.
NPV ϭ 0
1.355/12.5 ϭ .1084
NPV ϭ 0
NPV ϭϪ12.5 ϩ
1.355
.1084
ϭ 0
C ϭ $1.355
Cost of debt ( ) .08
Cost of equity ( ) .146
Marginal tax rate ( ) .35
Debt ratio (D/V)
Equity ratio (E/V)75/125 ϭ .6
50/125 ϭ .4
T

c
r
E
r
D
assets are worth $125 million. The cost of equity, , is the expected rate
of return from purchase of stock at $7.50 per share, the current market price. It
is not the return on book value per share. You can’t buy shares in Sangria for $5
anymore.
Sangria is consistently profitable and pays tax at the marginal rate of 35 percent.
That is the final input for Sangria’s WACC. The inputs are summarized here:
r
E
ϭ .146
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Calculate the expected dollar return to shareholders:
The project’s earnings are level and perpetual, so the expected rate of return on eq-
uity is equal to the expected equity income divided by the equity value:
The expected return on equity equals the cost of equity, so it makes sense that the
project’s NPV is zero.
Review of Assumptions
By discounting the perpetual crusher’s cash flows at Sangria’s WACC, we as-

sume that
• The project’s business risks are the same as Sangria’s other assets.
• The project supports the same fraction of debt to value as in Sangria’s overall
capital structure.
You can see the importance of these two assumptions: If the perpetual crusher had
greater business risk than Sangria’s other assets, or if acceptance of the project
would lead to a permanent, material
4
change in Sangria’s debt ratio, then Sangria’s
shareholders would not be content with a 14.6 percent expected return on their eq-
uity investment in the project.
We have illustrated the WACC formula only for a project offering perpetual
cash flows. But Miles and Ezzell have shown that the formula works for any
cash-flow pattern if the firm adjusts its borrowing to maintain a constant debt ra-
tio over time. When the firm departs from this borrowing policy, WACC is only
approximately correct.
5
ϭ
1.095
7.5
ϭ .146, or 14.6%
Expected equity return ϭ r
E
ϭ
expected equity income
equity value
Expected equity income ϭ C Ϫ 11 Ϫ T
c
2r
D

D ϭ 1.355 Ϫ .26 ϭ 1.095
After-tax interest ϭ r
D
11 Ϫ T
c
2D ϭ .0811 Ϫ .352 152ϭ .26
CHAPTER 19 Financing and Valuation 527
Perpetual Crusher (Market Values, millions)
Project value $12.5 $ 5.0 Debt (D)
7.5 Equity (E)
$12.5 $12.5 Project Value (V)
4
Users of WACC need not worry about small or temporary fluctuations in debt-to-value ratios.
Suppose that Sangria management decided for convenience to borrow $12.5 million to allow im-
mediate construction of the crusher. This does not necessarily change Sangria’s long-term financ-
ing policy. If the crusher supports only $5.0 million of debt, Sangria would have to pay down debt
to restore its overall debt ratio to 40 percent. For example, it could fund later projects with less debt
and more equity.
5
J. Miles and R. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Markets, and Project
Life: A Clarification,” Journal of Financial and Quantitative Analysis 15 (September 1980), pp. 719–730.
Suppose Sangria sets up this project as a mini-firm. Its market-value balance
sheet looks like this:
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation

© The McGraw−Hill
Companies, 2003
Sangria had just one asset and two sources of financing. A real company’s market
value balance sheet has many more entries, for example:
6
528 PART V Dividend Policy and Capital Structure
6
This balance sheet is for exposition and should not be confused with a real company’s books. It in-
cludes the value of growth opportunities, which accountants do not recognize, though investors do. It
excludes certain accounting entries, for example, deferred taxes.
Deferred taxes arise when a company uses faster depreciation for tax purposes than it uses in re-
ports to investors. That means the company reports more taxes than it pays. The difference is accumu-
lated as a liability for deferred taxes. In a sense there is a liability, because the Internal Revenue Service
“catches up,” collecting extra taxes, as assets age. But this is irrelevant in capital investment analysis,
which focuses on actual after-tax cash flows and uses accelerated tax depreciation.
Deferred taxes should not be regarded as a source of financing or an element of the weighted-average
cost of capital formula. The liability for deferred taxes is not a security held by investors. It is a balance
sheet entry created to serve the needs of accounting.
Deferred taxes can be important in regulated industries, however. Regulators take deferred taxes into
account in calculating allowed rates of return and the time patterns of revenues and consumer prices.
7
Financial practitioners have rules of thumb for deciding whether short-term debt is worth including
in the weighted-average cost of capital. Suppose, for example, that short-term debt is 10 percent of to-
tal liabilities and that net working capital is negative. Then short-term debt is almost surely being used
to finance long-term assets and should be explicitly included in WACC.
19.2 USING WACC—SOME TRICKS OF THE TRADE
Current assets, Current liabilities,
including cash, inventory, including accounts payable
and accounts receivable and short-term debt
Plant and equipment Long-term debt (D)

Preferred stock (P)
Growth opportunities Equity (E)
Firm value (V)
Several questions immediately arise:
1. How does the formula change when there are more than two sources of financing?
Easy: There is one cost for each element. The weight for each element is
proportional to its market value. For example, if the capital structure
includes both preferred and common shares,
where is investors’ expected rate of return on preferred stocks.
2. What about short-term debt? Many companies consider only long-term
financing when calculating WACC. They leave out the cost of short-term
debt. In principle this is incorrect. The lenders who hold short-term debt are
investors who can claim their share of operating earnings. A company that
ignores this claim will misstate the required return on capital investments.
But “zeroing out” short-term debt is not a serious error if the debt is
only temporary, seasonal, or incidental financing or if it is offset by holdings
of cash and marketable securities.
7
Suppose, for example, that your
company’s Italian subsidiary takes out a six-month loan from an Italian
bank to finance its inventory and accounts receivable. The dollar equivalent
r
P
WACC ϭ r
D
11 Ϫ T
c
2
D
V

ϩ r
P

P
V
ϩ r
E

E
V
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
of this loan will show up as a short-term debt on the parent’s balance sheet.
At the same time headquarters may be lending money by investing surplus
dollars in short-term securities. If lending and borrowing offset, there is no
point in including the cost of short-term debt in the weighted-average cost
of capital, because the company is not a net short-term borrower.
3. What about other current liabilities? Current liabilities are usually “netted out”
by subtracting them from current assets. The difference is entered as net
working capital on the left-hand side of the balance sheet. The sum of long-
term financing on the right is called total capitalization.
CHAPTER 19
Financing and Valuation 529

Net working capital
Long-term debt (D)
Plant and equipment Preferred stock (P)
Growth opportunities Equity (E)
Total capitalization (V)
Ϫ current liabilities
ϭ current assets
When net working capital is treated as an asset, forecasts of cash flows
for capital investment projects must treat increases in net working capital as
a cash outflow and decreases as an inflow. This is standard practice, which
we followed in Section 6.2.
Since current liabilities include short-term debt, netting them out
against current assets excludes the cost of short-term debt from the
weighted-average cost of capital. We have just explained why this can be an
acceptable approximation. But when short-term debt is an important,
permanent source of financing—as is common for small firms and firms
outside the United States—it should be shown explicitly on the right side of
the balance sheet, not netted out against current assets. The interest cost of
short-term debt is then one element of the weighted-average cost of capital.
4. How are the costs of the financing elements calculated? You can often use stock
market data to get an estimate of , the expected rate of return demanded
by investors in the company’s stock. With that estimate, WACC is not too
hard to calculate, because the borrowing rate and the debt and equity
ratios D/V and E/V can be directly observed or estimated without too much
trouble.
8
Estimating the value and required return for preferred shares is
likewise usually not too complicated.
Estimating the required return on other security types can be
troublesome. Convertible debt, where the investors’ return comes partly

from an option to exchange the debt for the company’s stock, is one
example. We will leave convertibles to Chapter 23.
Junk debt, where the risk of default is high, is likewise difficult. The
higher the odds of default, the lower the market price of the debt and the
higher the promised rate of interest. But the weighted-average cost of capital
r
D
r
E
8
Most corporate debt is not actively traded, so its market value cannot be observed directly. But you can
usually value a nontraded debt security by looking to securities that are traded and that have approxi-
mately the same default risk and maturity. See Chapter 24.
For healthy firms the market value of debt is usually not too far from book value, so many managers
and analysts use book value for D in the weighted-average cost of capital formula. However, be sure to
use market, not book, values for E.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
is an expected, that is, average, rate of return, not a promised one. For
example, in October 2001, Crown Cork bonds maturing in 2005 sold at only
76 percent of face value and offered an 18.6 percent promised yield, more
than 14 percentage points above yields on the highest-quality debt issues
maturing at the same time. The price and yield on the Crown Cork bond

demonstrated investors’ concern about the company’s chronic financial ill-
health. But the 18.6 percent yield was not an expected return, because it did
not average in the losses to be incurred if Crown Cork defaults. Including
18.6 percent as a “cost of debt” in a calculation of WACC would therefore
overstate Crown Cork’s true cost of capital.
This is bad news: There is no easy or tractable way of estimating the
expected rate of return on most junk debt issues.
9
The good news is that for
most debt the odds of default are small. That means the promised and
expected rates of return are close, and the promised rate can be used as an
approximation in the weighted-average cost of capital.
Industry Costs of Capital
You can also calculate WACC for industries. Suppose that a pharmaceutical com-
pany has a subsidiary that produces specialty chemicals. What discount rate is bet-
ter for the subsidiary’s projects—the company WACC or a weighted-average cost
of capital for a portfolio of “pure-play” specialty chemical companies? The latter
rate is better in principle and also in practice if good data are available for firms
with operations and markets similar to the subsidiary’s.
An Application to the Railroad Industry Every year the United States Surface
Transportation Board (STB) estimates a cost of capital for the railroad industry, de-
fined as Class I (big) railroads. We will use the STB’s data and estimates to calcu-
late a railroad industry WACC for 1999.
The STB took care to estimate the market value of the railroads’ common shares
and all outstanding debt issues, including debt-equivalents such as equipment trust
certificates and financial leases.
10
The aggregate industry capital structure was
11
530 PART V Dividend Policy and Capital Structure

9
When betas can be estimated for the junk issue or for a sample of similar issues, the expected return
can be calculated from the capital asset pricing model. Otherwise, the yield should be adjusted for the
probability of default. Evidence on historical default rates on junk bonds is described in Chapter 25.
10
Equipment trust certificates are described in Section 25.3; financial leases are discussed in Chapter 26.
11
There were three tiny preferred issues. For simplicity we have added them to debt.
Market Value (billions) Financing Weights
Debt $31,627.8 37.3%
Equity 53,210.0 62.7
The average cost of debt was 7.2 percent. To estimate the cost of equity, the STB used
the constant-growth DCF model, which you will recall with pleasure from Section
4.3. If investors expect dividends to grow at a constant, perpetual rate, g, then the ex-
pected return is the sum of the dividend yield and the expected growth rate:
r
E
ϭ
DIV
1
P
0
ϩ g
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation

© The McGraw−Hill
Companies, 2003
An investor who bought a portfolio of the shares of Class I railroads in 1999 got a
dividend yield of about 2.0 percent. A review of security analysts’ forecasts gave
an average expected growth rate for earnings and dividends of 10.9 percent. The
cost of equity was thus estimated at r
E
ϭ 2.0 ϩ 10.9 ϭ 12.9 percent.
Using the statutory marginal tax rate of 35 percent,
12
the railroad industry
WACC is
Valuing Companies: WACC vs. the Flow-to-Equity Method
WACC is normally used as a hurdle rate or discount rate to value proposed capi-
tal investments. But sometimes it is used as a discount rate for valuing whole com-
panies. For example, the financial manager may need to value a target company to
decide whether to go ahead with a merger.
Valuing companies raises no new conceptual problems. You just treat the com-
pany as if it were one big project. Forecast the company’s cash flows (the hardest
part of the exercise) and discount back to present value. The company’s WACC is
the right discount rate if the company’s debt ratio is expected to remain reasonably
close to constant. But remember:
• If you discount at WACC, cash flows have to be projected just as you would
for a capital investment project. Do not deduct interest. Calculate taxes as if
the company were all-equity-financed. The value of interest tax shields is
picked up in the WACC formula.
• The company’s cash flows will probably not be forecasted to infinity. Financial
managers usually forecast to a medium-term horizon—10 years, say—and add
a terminal value to the cash flows in the horizon year. The terminal value is
the present value at the horizon of post-horizon flows. Estimating the terminal

value requires careful attention because it often accounts for the majority of
the value of the company. See Section 4.5.
• Discounting at WACC values the assets and operations of the company. If the
object is to value the company’s equity, that is, its common stock, don’t forget
to subtract the value of the company’s outstanding debt.
If the task is to value equity, there’s an obvious alternative to discounting com-
pany cash flows at its WACC. Discount the cash flows to equity, after interest and af-
ter taxes, at the cost of equity. This is called the flow-to-equity method. If the com-
pany’s debt ratio is constant over time, the flow-to-equity method should give the
same answer as discounting company cash flows at the WACC and subtracting debt.
The flow-to-equity method seems simple, and it is simple if the proportions of
debt and equity financing stay reasonably close to constant for the life of the com-
pany. But the cost of equity depends on financial leverage; it depends on financial
risk as well as business risk. If financial leverage will change significantly, dis-
counting flows to equity at today’s cost of equity will not give the right answer.
A one-shot change in financing can usually be accommodated. Think again of a
proposed takeover. Suppose the financial manager decides that the target’s 20 per-
cent debt-to-value ratio is stodgy and too conservative. She decides the company
WACC ϭ 0.07211Ϫ.3521.3732ϩ .1291.6272ϭ .098, or about 10%
CHAPTER 19
Financing and Valuation 531
12
The STB actually uses a pretax cost of debt. If the STB’s reported WACC is used as a discount rate, in-
terest tax shields have to be valued separately, as in the adjusted-present-value method described in
Section 19.4.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure

19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
could easily support 40 percent debt and asks you to value the target’s shares on
that assumption. Unfortunately you have estimated the cost of equity at the exist-
ing 20 percent ratio. No problem! Adjust the cost of equity (we will revisit the for-
mula in the next section) and proceed as usual. Of course you must forecast and
discount cash flows to equity at the new 40 percent debt ratio. You also have to as-
sume that this debt ratio will be maintained after the takeover.
Mistakes People Make in Using the Weighted-Average Formula
The weighted-average formula is very useful but also dangerous. It tempts people
to make logical errors. For example, manager Q, who is campaigning for a pet proj-
ect, might look at the formula
and think, Aha! My firm has a good credit rating. It could borrow, say, 90 percent of
the project’s cost if it likes. That means and . My firm’s borrowing
rate is 8 percent, and the required return on equity, , is 15 percent. Therefore
or 6.2 percent. When I discount at that rate, my project looks great.
Manager Q is wrong on several counts. First, the weighted-average formula
works only for projects that are carbon copies of the firm. The firm isn’t 90 percent
debt-financed.
Second, the immediate source of funds for a project has no necessary connection
with the hurdle rate for the project. What matters is the project’s overall contribu-
tion to the firm’s borrowing power. A dollar invested in Q’s pet project will not in-
crease the firm’s debt capacity by $.90. If the firm borrows 90 percent of the pro-
ject’s cost, it is really borrowing in part against its existing assets. Any advantage
from financing the new project with more debt than normal should be attributed
to the old projects, not to the new one.
Third, even if the firm were willing and able to lever up to 90 percent debt, its cost
of capital would not decline to 6.2 percent (as Q’s naive calculation predicts). You

cannot increase the debt ratio without creating financial risk for stockholders and
thereby increasing , the expected rate of return they demand from the firm’s com-
mon stock. Going to 90 percent debt would certainly increase the borrowing rate, too.
r
E
WACC ϭ .0811 Ϫ .352 1.92ϩ .151.12ϭ .062
r
E
r
D
E/V ϭ .1D/V ϭ .9
WACC ϭ r
D
11 Ϫ T
c
2
D
V
ϩ r
E

E
V
532 PART V
Dividend Policy and Capital Structure
13
It could change the tax rate too. For example, the firm might have enough pretax income to cover in-
terest payments at 20 percent debt but not at 40 percent. In this case the effective marginal tax rate would
be higher at 20 percent debt.
19.3 ADJUSTING WACC WHEN DEBT RATIOS OR

BUSINESS RISKS CHANGE
The WACC formula assumes that the project to be valued will be financed in the
same proportions of debt and equity as the firm as a whole. What if that is not true?
What if the perpetual crusher project supports debt equal to, say, 20 percent of proj-
ect value, versus 40 percent debt financing for the firm as a whole?
Moving from 40 to 20 percent debt changes all the elements of the WACC for-
mula except the tax rate.
13
Obviously the financing weights change. But the cost
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of equity is less, because financial risk is reduced. The cost of debt may be
lower too.
Figure 19.1 plots WACC and the costs of debt and equity as a function of the
debt–equity ratio. The flat line is r, the opportunity cost of capital. Remember, this
is the expected rate of return that investors would want from the project if it were
all-equity-financed. The opportunity cost of capital depends only on business risk
and is the natural reference point.
Suppose Sangria or the perpetual crusher project were all-equity-financed
( ). At that point WACC equals cost of equity, and both equal the opportu-
nity cost of capital. Start from that point in Figure 19.1. As the debt ratio increases,
the cost of equity increases, because of financial risk, but notice that WACC de-
clines. The decline is not caused by use of “cheap” debt in place of “expensive” eq-

uity. It falls because of the tax shields on debt interest payments. If there were no
corporate income taxes, the weighted-average cost of capital would be constant,
and equal to the opportunity cost of capital, at all debt ratios. We showed this in
Chapters 9 and 17.
Figure 19.1 shows the shape of the relationship between financing and WACC,
but we have numbers only for Sangria’s current 40 percent debt ratio. We want to
recalculate WACC at a 20 percent ratio.
Here is the simplest way to do it. There are three steps.
Step 1 Calculate the opportunity cost of capital. In other words, calculate WACC
and the cost of equity at zero debt. This step is called unlevering the WACC. The
simplest unlevering formula is
This formula comes directly from Modigliani and Miller’s proposition I (see Sec-
tion 17.1). If taxes are left out, the weighted-average cost of capital equals the op-
portunity cost of capital and is independent of leverage.
Opportunity cost of capital ϭ r ϭ r
D
D/V ϩ r
E
E/V
D/V ϭ 0
r
E
CHAPTER 19 Financing and Valuation 533
r
Debt–equity
ratio (
D/E

)
Cost of equity (

r
E

)
Cost of debt (
r
D
)
Opportunity cost of capital (
r
)
Rates of
return
WACC
FIGURE 19.1
WACC plotted against the debt–
equity ratio. WACC equals the
opportunity cost of capital when
there is no debt. WACC declines
with financial leverage because
of interest tax shields.
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Step 2 Estimate the cost of debt, , at the new debt ratio, and calculate the new
cost of equity.
This formula is Modigliani and Miller’s proposition II (see Section 17.2). It calls for
D/E, the ratio of debt to equity, not debt to value.
Step 3 Recalculate the weighted-average cost of capital at the new financing
weights.
Let’s do the numbers for the perpetual crusher project at or 20 percent.
Step 1. Sangria’s current debt ratio is
Step 2. We will assume that the debt cost stays at 8 percent when the debt ratio
is 20 percent. Then
Note that the debt–equity ratio is .
Step 3. Recalculate WACC.
Figure 19.2 enters these numbers on the plot of WACC versus debt ratio. The 11.4
percent project discount rate at 20 percent debt to value is .56 percentage points
higher than at 40 percent.
Another Example: WACC for U.S. Railroads at 45 percent Debt Let’s return to the
WACC we calculated for large U.S. railroads. We assumed a debt-to-value ratio of
37.3 percent. How would the railroad industry WACC change at 45 percent debt?
WACC ϭ .0811 Ϫ .352
1.22ϩ .131.82ϭ .114 or 11.4%
.2/.8 ϭ .25
r
E
ϭ .12 ϩ 1.12 Ϫ .082 1.252ϭ .13 or 13%
r ϭ .08 1.42ϩ .1461.62ϭ .12 or 12%
D/V ϭ .4
D/V ϭ .20
r
E
ϭ r ϩ 1r Ϫ r

D
2D/E
r
D
534 PART V Dividend Policy and Capital Structure
12
8
.25
(
D/V
= .2)
.67
(
D/V
= .4)
10
14
13.0
11.4
8.0
14.6
10.84
8.0
Debt–equity
ratio (
D/E

)
Cost of equity (
r

E

)
Cost of debt (
r
D

)
Opportunity cost of capital (
r
= 12%)
Rates of
return, percent
WACC
FIGURE 19.2
This plot shows WACC for
the Sangria Corporation at
debt-to-equity ratios of 25
and 67 percent. The corre-
sponding debt-to-value
ratios are 20 and 40 percent.
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Step 1. Calculate the unlevered opportunity cost of capital
Step 2. Assume that the cost of debt increases to 8 percent at 45 percent debt. The
cost of equity is
Step 3. Recalculate WACC. If the marginal tax rate stays at 35 percent,
The cost of capital drops by more than one half percentage point. Is this a great
deal? Not as good as it looks. In these simple calculations, the cost of capital drops
as financial leverage increases, but only because of corporate interest tax shields.
In Chapter 18 we reviewed all the reasons why just focusing on corporate interest
tax shields overstates the advantages of debt. For example, costs of financial dis-
tress encountered at high debt levels appear nowhere in the WACC formula or in
the standard formulas relating the cost of equity for leverage.
14
Unlevering and Relevering Betas
Our three-step procedure (1) unlevers and then (2) relevers the cost of equity. Some
financial managers find it convenient to (1) unlever and then (2) relever the equity
beta. Given the beta of equity at the new debt ratio, the cost of equity is determined
from the capital asset pricing model. Then WACC is recalculated.
The formula for unlevering beta was given in Section 9.2.
This equation says that the beta of a firm’s assets is revealed by the beta of a port-
folio of all of the firm’s outstanding debt and equity securities. An investor who
bought such a portfolio would own the assets free and clear and absorb only busi-
ness risks.
The formula for relevering beta closely resembles MM’s proposition II, except
that betas are substituted for rates of return:
The Importance of Rebalancing
The formulas for WACC and for unlevering and relevering expected returns are
simple, but we must be careful to remember underlying assumptions. The most
important point is rebalancing.
Calculating WACC for a company at its existing capital structure requires that the
capital structure not change; in other words, the company must rebalance its capital

structure to maintain the same market-value debt ratio for the relevant future. Take
Sangria Corporation as an example. It starts with a debt-to-value ratio of 40 percent
and a market value of $125 million. Suppose that Sangria’s products do unexpectedly
␤
equity
ϭ ␤
asset
ϩ 1␤
asset
Ϫ ␤
debt
2D/E
␤
asset
ϭ ␤
debt
1D/V2ϩ ␤
equity
1E/V2
WACC ϭ .08011 Ϫ .352.45 ϩ .1301.552ϭ .095 or 9.5%
r
E
ϭ .108 ϩ 1.108 Ϫ .080245/55 ϭ .13
r ϭ .0721.3732ϩ .1291.6272ϭ .108
CHAPTER 19 Financing and Valuation 535
14
Some financial managers and analysts argue that the costs of debt and equity increase rapidly at high
debt ratios because of costs of financial distress. This in turn would cause the WACC curve in Figure
19.1 to flatten out, and finally increase, as the debt ratio climbs. For practical purposes, this can be a sen-
sible end result. However, formal modeling of the interactions between the cost of financial distress and

the expected rates of return on the company’s securities is not easy.
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well in the marketplace and that market value increases to $150 million. Rebalancing
means that it will then increase debt to ,
15
thus regaining a
40 percent ratio. If market value instead falls, Sangria would have to pay down debt
proportionally.
Of course real companies do not rebalance capital structure in such a mechani-
cal and compulsive way. For practical purposes, it’s sufficient to assume gradual
but steady adjustment toward a long-run target. But if the firm plans significant
changes in capital structure (for example, if it plans to pay off its debt), the WACC
formula won’t work. In such cases, you should turn to the APV method, which we
describe in the next section.
Our three-step procedure for recalculating WACC makes a similar rebalancing as-
sumption.
16
Whatever the starting debt ratio, the firm is assumed to rebalance to main-
tain that ratio in the future. The unlevering and relevering in steps 1 and 2 also ignore
any impact of investors’ personal income taxes on the costs of debt and equity.
17
.4 ϫ 150 ϭ $60 million

536 PART V Dividend Policy and Capital Structure
15
The proceeds of the additional borrowing would be paid out to shareholders or used, along with ad-
ditional equity investment, to finance Sangria’s growth.
16
Similar, but not identical. The basic WACC formula assumes that rebalancing occurs at the end of each
period. The unlevering and relevering formulas used in steps 1 and 2 of our three-step procedure are
exact only if rebalancing is continuous so that the debt ratio stays constant day-to-day and week-to-
week. However, the errors introduced from annual rebalancing are very small and can be ignored for
practical purposes.
17
The response of the cost of equity to changes in financial leverage can be affected by personal taxes.
This is not covered here and is rarely adjusted for in practice.
19.4 ADJUSTED PRESENT VALUE
We now take a different tack. Instead of messing around with the discount rate, we
explicitly adjust cash flows and present values for costs or benefits of financing.
This approach is called adjusted present value, or APV.
The adjusted-present-value rule is easiest to understand in the context of simple
numerical examples. We start by analyzing a project under base-case assumptions
and then consider possible financing side effects of accepting the project.
The Base Case
The APV method begins by valuing the project as if it were a mini-firm financed
solely by equity. Consider a project to produce solar water heaters. It requires a $10
million investment and offers a level after-tax cash flow of $1.8 million per year for
10 years. The opportunity cost of capital is 12 percent, which reflects the project’s
business risk. Investors would demand a 12 percent expected return to invest in the
mini-firm’s shares.
Thus the mini-firm’s base-case NPV is
Considering the project’s size, this figure is not much greater than zero. In a pure
MM world where no financing decision matters, the financial manager would lean

toward taking the project but would not be heartbroken if it were discarded.
NPV ϭϪ10 ϩ
a
10
tϭ1

1.8
11.122
t
ϭϩ$.17 million, or $170,000
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Issue Costs
But suppose that the firm actually has to finance the $10 million investment by is-
suing stock (it will not have to issue stock if it rejects the project) and that issue
costs soak up 5 percent of the gross proceeds of the issue. That means the firm has
to issue $10,526,000 in order to obtain $10,000,000 cash. The $526,000 difference
goes to underwriters, lawyers, and others involved in the issue process.
The project’s APV is calculated by subtracting the issue cost from base-case NPV:
The firm would reject the project because APV is negative.
Additions to the Firm’s Debt Capacity
Consider a different financing scenario. Suppose that the firm has a 50 percent tar-
get debt ratio. Its policy is to limit debt to 50 percent of its assets. Thus, if it invests

more, it borrows more; in this sense investment adds to the firm’s debt capacity.
18
Is debt capacity worth anything? The most widely accepted answer is yes be-
cause of the tax shields generated by interest payments on corporate borrowing.
(Look back to our discussion of debt and taxes in Chapter 18.) For example, MM’s
theory states that the value of the firm is independent of its capital structure except
for the present value of interest tax shields:
This theory tells us to compute the value of the firm in two steps: First compute its
base-case value under all-equity financing, and then add the present value of taxes
saved due to a departure from all-equity financing. This procedure is like an APV
calculation for the firm as a whole.
We can repeat the calculation for a particular project. For example, suppose that
the solar heater project increases the firm’s assets by $10 million and therefore
prompts it to borrow $5 million more. Suppose that this $5 million loan is repaid
in equal installments, so that the amount borrowed declines with the depreciating
book value of the solar heater project. We also assume that the loan carries an in-
terest rate of 8 percent. Table 19.1 shows how the value of the interest tax shields is
calculated. This is the value of the additional debt capacity contributed to the firm
by the project. We obtain APV by adding this amount to the project’s NPV:
With these numbers, the solar heater project looks like a “go.” But notice the dif-
ferences between this APV calculation and an NPV calculated with a WACC used as
the discount rate. The APV calculation assumes debt equal to 50 percent of book
value, paid down on a fixed schedule. NPV using WACC assumes debt is a constant
fraction of market value in each year of the project’s life. Since the project’s value will
inevitably turn out higher or lower than expected, using WACC also assumes that
ϭϩ170,000 ϩ 576,000 ϭ $746,000
APV ϭ base-case NPV ϩ PV1tax shield2
Firm value ϭ value with all-equity financing ϩ PV1tax shield2
ϭϩ170,000 Ϫ 526,000 ϭϪ$356,000
APV ϭ base-case NPV Ϫ issue cost

CHAPTER 19
Financing and Valuation 537
18
Debt capacity is potentially misleading because it seems to imply an absolute limit to the amount the
firm is able to borrow. That is not what we mean. The firm limits borrowing to 50 percent of assets as a
rule of thumb for optimal capital structure. It could borrow more if it wanted to run increased risks of
costs of financial distress.
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future debt levels will be increased or reduced as necessary to keep the future debt
ratio constant.
APV can be used when debt supported by a project is tied to the project’s book
value or has to be repaid on a fixed schedule. For example, Kaplan and Ruback used
APV to analyze the prices paid for a sample of leveraged buyouts (LBOs). LBOs are
takeovers, typically of mature companies, financed almost entirely with debt. How-
ever, the new debt is not intended to be permanent. LBO business plans call for gen-
erating extra cash by selling assets, shaving costs, and improving profit margins. The
extra cash is used to pay down the LBO debt. Therefore you can’t use WACC as a dis-
count rate to evaluate an LBO because its debt ratio will not be constant.
APV works fine for LBOs. The company is first evaluated as if it were all-equity-
financed. That means that cash flows are projected after tax, but without any in-
terest tax shields generated by the LBO’s debt. The tax shields are then valued sep-
arately. The debt repayment schedule is set down in the same format as Table 19.1

and the present value of interest tax shields is calculated and added to the all-
equity value. Any other financing side effects are added also. The result is an APV
valuation for the company.
19
Kaplan and Ruback found that APV did a pretty good
job explaining prices paid in these hotly contested takeovers, considering that not
all the information available to bidders had percolated into the public domain.
Kaplan and Ruback were restricted to publicly available data.
538 PART V
Dividend Policy and Capital Structure
Debt Outstanding Interest Present Value
Year at Start of Year Interest Tax Shield of Tax Shield
1 $5,000 $400 $140 $129.6
2 4,500 360 126 108.0
3 4,000 320 112 88.9
4 3,500 280 98 72.0
5 3,000 240 84 57.2
6 2,500 200 70 44.1
7 2,000 160 56 32.6
8 1,500 120 42 22.7
9 1,000 80 28 14.0
10 500 40 14 6.5
Total $576
TABLE 19.1
Calculating the present value of interest tax shields on debt supported by the solar heater project
(dollar figures in thousands).
Assumptions:
1. Marginal tax ; tax shield .
2. Debt principal is repaid at end of year in ten $500,000 installments.
3. Interest rate on debt is 8 percent.

4. Present value is calculated at the 8 percent borrowing rate. The assumption here is that the tax shields are just as
risky as the interest payments generating them.
ϭ T
c
ϫ interestrate ϭ T
c
ϭ .35
19
Kaplan and Ruback actually used “compressed” APV, in which all cash flows, including interest tax
shields, are discounted at the opportunity cost of capital. S. N. Kaplan and R. S. Ruback, “The Valua-
tion of Cash Flow Forecasts: An Empirical Analysis,” Journal of Finance 50 (September 1995),
pp. 1059–1093.
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The Value of Interest Tax Shields
In Table 19.1, we boldly assume that the firm can fully capture interest tax shields
of $.35 on every dollar of interest. We also treat the interest tax shields as safe cash
inflows and discount them at a low 8 percent rate.
The true present value of the tax shields is almost surely less than $576,000:
• You can’t use tax shields unless you pay taxes, and you don’t pay taxes unless
you make money. Few firms can be sure that future profitability will be
sufficient to use up the interest tax shields.
• The government takes two bites out of corporate income: the corporate tax

and the tax on bondholders’ and stockholders’ personal income. The corporate
tax favors debt; the personal tax favors equity.
• A project’s debt capacity depends on how well it does. When profits exceed
expectations, the firm can borrow more; if the project fails, it won’t support
any debt. If the future amount of debt is tied to future project value, then the
interest tax shields given in Table 19.1 are estimates, not fixed amounts.
In Chapter 18, we argued that the effective tax shield on interest was probably
not 35 percent ( ) but some lower figure, call it T*. We were unable to pin
down an exact figure for T*.
Suppose, for example, that we believe T* ϭ .25. We can easily recalculate the
APV of the solar heater project. Just multiply the present value of the interest tax
shields by 25/35. The bottom line of Table 19.1 drops from $576,000 to
. APV drops to
PV(tax shield) drops still further if the tax shields are treated as forecasts and
discounted at a higher rate. Suppose the firm ties the amount of debt to actual fu-
ture project cash flows. Then the interest tax shields become just as risky as the
project and should be discounted at the 12 percent opportunity cost of capital.
PV(tax shield) drops to $362,000 at T* ϭ .25.
Review of the Adjusted-Present-Value Approach
If the decision to invest in a capital project has important side effects on other fi-
nancial decisions made by the firm, those side effects should be taken into account
when the project is evaluated. They include interest tax shields on debt supported
by the project (a plus), any issue costs of raising financing for the project (a minus),
or perhaps other side effects such as the value of a government-subsidized loan
tied to the project.
The idea behind APV is to divide and conquer. The approach does not attempt
to capture all the side effects in a single calculation. A series of present value cal-
culations is made instead. The first establishes a base-case value for the project: its
value as a separate, all-equity-financed mini-firm. Then each side effect is traced
out, and the present value of its cost or benefit to the firm is calculated. Finally, all

the present values are added together to estimate the project’s total contribution to
the value of the firm. Thus, in general,
Project APV ϭ base-case NPV ϩ
sum of the present values of the side
effects of accepting the project
ϭϩ170,000 ϩ 411,000 ϭ $581,000
APV ϭ base-case NPV ϩ PV1tax shield2
576,000125/352ϭ $411,000
T
c
ϭ .35
CHAPTER 19 Financing and Valuation 539
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The wise financial manager will want to see not only the adjusted present value
but also where that value is coming from. For example, suppose that base-case
NPV is positive but the benefits are outweighed by the costs of issuing stock to fi-
nance the project. That should prompt the manager to look around to see if the
project can be rescued by an alternative financing plan.
APV for International Projects
APV is most useful when financing side effects are numerous and important. This
is frequently the case for large international projects, which may have custom-
tailored project financing and special contracts with suppliers, customers, and gov-

ernments.
20
Here are a few examples of financing side effects encountered in the
international arena.
We explain project finance in Chapter 25. It typically means very high debt ra-
tios to start, with most or all of a project’s early cash flows committed to debt ser-
vice. Equity investors have to wait. Since the debt ratio will not be constant, you
have to turn to APV.
Project financing may include debt available at favorable interest rates. Most
governments subsidize exports by making special financing packages available,
and manufacturers of industrial equipment may stand ready to lend money to help
close a sale. Suppose, for example, that your project requires construction of an on-
site electricity generating plant. You solicit bids from suppliers in various coun-
tries. Don’t be surprised if the competing suppliers sweeten their bids with offers
of low interest rate project loans or if they offer to lease the plant on favorable
terms. You should then calculate the NPVs of these loans or leases and include
them in your project analysis.
Sometimes international projects are supported by contracts with suppliers or
customers. Suppose a manufacturer wants to line up a reliable supply of a crucial
raw material—powdered magnoosium, say. The manufacturer could subsidize a
new magnoosium smelter by agreeing to buy 75 percent of production and guar-
anteeing a minimum purchase price. The guarantee is clearly a valuable addition
to project APV: If the world price of powdered magnoosium falls below the mini-
mum, the project doesn’t suffer. You would calculate the value of this guarantee
(by the methods explained in Chapters 20 and 21) and add it to APV.
Sometimes local governments impose costs or restrictions on investment or disin-
vestment. For example, Chile, in an attempt to slow down a flood of short-term cap-
ital inflows in the 1990s, required investors to “park” part of their incoming money in
non-interest-bearing accounts for a period of two years. An investor in Chile during
this period would calculate the cost of this requirement and subtract it from APV.

APV for the Perpetual Crusher Project
Discounting at WACC and calculating APV may seem like totally disconnected ap-
proaches to valuation. But we can show that, with consistent assumptions, they
give nearly identical answers. We demonstrate this for the perpetual crusher proj-
ect introduced in Section 19.1.
In the following calculations, we ignore any issue costs and concentrate on the
value of interest tax shields. To keep things simple, we assume throughout this sec-
540 PART V
Dividend Policy and Capital Structure
20
Use of APV for international projects was first advocated by D. L. Lessard, “Valuing Foreign Cash
Flows: An Adjusted Present Value Approach,” in D. L. Lessard, ed., International Financial Management:
Theory and Application, Warren, Gorham and Lamont, Boston, MA, 1979.
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tion that the only financing side effects are the interest tax shields on debt supported
by the perpetual crusher project, and we consider corporate taxes only. (In other
words, .) As in Section 19.1, we assume that the perpetual crusher is an exact
match, in business risk and financing, to its parent, the Sangria Corporation.
Base-case NPV is found by discounting after-tax project cash flows of $1.355 mil-
lion at the opportunity cost of capital r of 12 percent and then subtracting the $12.5
million outlay. The cash flows are perpetual, so
Thus the project would not be worthwhile with all-equity financing. But it actually

supports debt of $5 million. At an 8 percent borrowing rate ( ) and a 35 percent
tax rate ( ), annual interest tax shields are , or $140,000.
What are those tax shields worth? It depends on the financing rule the company
follows. There are two common rules:
• Financing Rule 1: Debt fixed. Borrow a fraction of initial project value and make
any debt repayments on a predetermined schedule. We followed this rule in
Table 19.1.
• Financing Rule 2: Debt rebalanced. Adjust the debt in each future period to keep
it at a constant fraction of future project value.
What do these rules mean for the perpetual crusher project? Under Financing
Rule 1, debt stays at $5 million come hell or high water, and interest tax shields stay
at $140,000 per year. The tax shields are tied to fixed interest payments, so the 8 per-
cent cost of debt is a reasonable discount rate:
If the perpetual crusher were financed solely by equity, project value would be
$11.29 million. With fixed debt of $5 million, value increases by PV(tax shield) to
.
Under Financing Rule 2, debt is rebalanced to 40 percent of actual project value.
That means future debt levels are not known at the start of the project. They shift
up or down depending on the success or failure of the project. Interest tax shields
therefore pick up the project’s business risk.
If interest tax shields are just as risky as the project, they should be discounted
at the project’s opportunity cost of capital, in this case 12 percent.
We have now valued the perpetual crusher project three different ways:
1. APV (debt fixed) ϭ ϩ$.54 million.
2. APV (debt rebalanced)ϭ Ϫ$.04 million.
3. NPV (discounting at WACC)ϭ $0 million.
The first APV is the highest, because it assumes that debt is fixed, not rebalanced,
and that interest tax shields are as safe as the interest payments generating them.
APV 1debt rebalanced2ϭϪ1.21 ϩ 1.17 ϭϪ$.04 million
PV1tax shields,

debt rebalanced2ϭ
140,000
.12
ϭ 1, 170,000, or $1.17 million
11.29 ϩ 1.75 ϭ $13.04 million
ϭϪ1.21 ϩ 1.75 ϭϩ$.54
million
APV ϭ base-case NPV ϩ PV1tax shield2
PV1tax shields, debt fixed2ϭ
140,000
.08
ϭ $1,750,000, or $1.75 million
.35 ϫ .08 ϫ 5 ϭ .14T
c
ϭ .35
r
D
ϭ .08
Base-case NPV ϭϪ12.5 ϩ
1.355
.12
ϭϪ$1.21 million
T* ϭ T
c
CHAPTER 19 Financing and Valuation 541
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure

19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
A Technical Point on Financing Rule 2
But why don’t APV calculations 2 and 3, which both follow Financing Rule 2, gen-
erate the same number? The answer is that our calculation of APV (debt rebal-
anced) gets the implications of Financing Rule 2 only approximately right.
Even when debt is rebalanced, next year’s interest tax shields are fixed. Year 1’s in-
terest tax shield is fixed by the amount of debt at date 0, the start of the project. There-
fore, year 1’s interest tax shield should have been discounted at 8, not 12 percent.
Year 2’s interest tax shield is not known at the start of the project, since debt is
rebalanced at date 1, depending on the first year’s performance. But once date 1’s
debt level is set, the interest tax shield is known. Therefore the forecasted interest
tax shield at date 2 ($140,000) should be discounted for one year at 12 percent and
one year at 8 percent.
The reasoning repeats. Every year, once debt is rebalanced, next year’s interest tax
shield is fixed. For example, year 15’s interest tax shield is fixed once debt is rebal-
anced in year 14. Thus the present value of the year 15 tax shield is the date 0 fore-
cast (again $140,000) discounted one year at 8 percent and 14 years at 12 percent.
So the procedure for calculating the exact value of tax shields under Financing
Rule 2 is as follows:
1. Discount at the opportunity cost of capital, because future tax shields are
tied to actual cash flows.
2. Multiply the resulting PV by , because the tax shields are
fixed one period before receipt.
For the perpetual crusher project, the forecasted interest tax shields are $140,000
or $.14 million. Their exact value is
The APV of the project, given these assumptions about future debt capacity, is
This calculation exactly matches our first valuation of the perpetual crusher proj-

ect based on WACC. Discounting at WACC implicitly recognizes that next year’s
interest tax shield is fixed by this year’s debt level.
21
ϭϪ1.21 ϩ 1.21 ϭ $0 million
APV ϭ base-case NPV ϩ PV1tax shield2
PV1exact2ϭ 1.17 ϫ a
1.12
1.08
bϭ $1.21 million
PV1approximate2ϭ
.14
.12
ϭ $1.17 million
11 ϩ r2/11 ϩ r
D
2
542 PART V Dividend Policy and Capital Structure
21
Miles and Ezzell (see footnote 5) have come up with a useful formula for modifying WACC:
where L is the debt-to-value ratio and is the net tax saving per dollar of interest paid. In practice
is hard to pin down, so the marginal tax rate is used instead.
The Miles–Ezzell formula assumes Financing Rule 2, that is, that debt is rebalanced at the end of
every period (although next year’s interest tax shield is fixed). You can check that it values the Sangria
project exactly .
In Section 19.3, we used a three-step procedure to calculate WACC at different debt ratios. It turns
out that this procedure is not exactly the same as the changes in WACC calculated by the Miles–Ezzell
formula. However, the numerical differences are in practice very small. In the Sangria example they are
lost in rounding.
1NPV ϭ $0 million2
T

c
T*T*
WACC ϭ r Ϫ Lr
D
T* a
1 ϩ r
1 ϩ r
D
b
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Which Financing Rule?
In practice it rarely pays to worry whether interest tax shields are valued approxi-
mately or exactly ($0 million). Your worrying time
will be much better spent in refining forecasts of operating cash flows and think-
ing through what-if scenarios.
But which financing rule is better—debt fixed or debt rebalanced?
Sometimes debt has to be paid down on a fixed schedule, as for the solar heater
project in Table 19.1. This is the case for most LBOs. But as a general rule we vote
for the assumption of rebalancing, that is, for Financing Rule 2. Any capital bud-
geting procedure that assumes debt levels are always fixed after a project is under-
taken is grossly oversimplified. Should we assume that the perpetual crusher proj-
ect contributes $5 million to the firm’s debt capacity not just when the project is

undertaken but from here to eternity? That amounts to saying that the future value
of the project will not change—a strong assumption indeed.
Financing Rule 2 is better: not “Always borrow $5 million,” but “Always bor-
row 40 percent of the perpetual crusher project value.” Then if project value in-
creases, the firm borrows more. If it decreases, the firm borrows less. Under this
policy you can no longer discount future interest tax shields at the borrowing rate
because the shields are no longer certain. Their size depends on the amount actu-
ally borrowed and, therefore, on the actual future value of the project.
APV and Hurdle Rates
APV tells you whether a project makes a net contribution to the value of the firm.
It can also tell you a project’s break-even cash flow or internal rate of return. Let’s
check this for the perpetual crusher project. We first calculate the income at which
. We will then determine the project’s minimum acceptable internal rate
of return (IRR).
or 10.84 percent of the $12.5 million outlay. In other words, the minimum accept-
able IRR for the project is 10.84 percent. At this IRR project APV is zero.
Suppose that we encounter another project with perpetual cash flows. Its op-
portunity cost of capital is also , and it also expands the firm’s borrowing
power by 40 percent of project value. We know that if such a project offers an IRR
greater than 10.84 percent, it will have a positive APV. Therefore, we could shorten
the analysis by just discounting the project’s cash inflows at 10.84 percent.
22
This
discount rate is the adjusted cost of capital. It reflects both the project’s business risk
and its contribution to the firm’s debt capacity.
We will call the adjusted cost of capital . To calculate we find the minimum
acceptable internal rate of return—the IRR at which . The rule is this: Ac-
cept projects which have a positive NPV at the adjusted cost of capital .r*
APV ϭ 0
r*r*

r ϭ .12
Annual income ϭ $1.355 million
ϭ
annual income
.12
Ϫ 12.5 ϩ 1.21 ϭ 0
APV ϭ
annual income
r
Ϫ investment ϩ PV1tax shield2
APV ϭ 0
1giving APV ϭϪ$.04 million2
CHAPTER 19 Financing and Valuation 543
22
Remember that forecasted project cash flows do not reflect the tax shields generated by any debt the
project may support. Project taxes are calculated assuming all-equity financing.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
The 10.84 percent adjusted cost of capital for the perpetual crusher project is (no
surprise) identical to Sangria Corporation’s WACC, calculated in Section 19.1.
A General Definition of the Adjusted Cost of Capital
We recapitulate the two concepts of cost of capital:
• Concept 1: The opportunity cost of capital (r). This is the expected rate of return

offered in capital markets by equivalent-risk assets. This depends on the risk
of the project’s cash flows. The opportunity cost of capital is the correct
discount rate for the project if it is all-equity-financed.
• Concept 2: The adjusted cost of capital (r*). This is an adjusted opportunity cost
or hurdle rate that reflects the financing side effects of an investment project.
Some people just say “cost of capital.” Sometimes their meaning is clear in con-
text. At other times, they don’t know which concept they are referring to, and that
can sow widespread confusion.
When financing side effects are important, you should accept projects with pos-
itive APVs. But if you know the adjusted discount rate, you don’t have to calculate
APV: You just calculate NPV at the adjusted rate. The weighted-average cost of
capital formula is the most common way to calculate the adjusted cost of capital.
544 PART V
Dividend Policy and Capital Structure
19.5 DISCOUNTING SAFE, NOMINAL CASH FLOWS
Suppose you’re considering purchase of a $100,000 machine. The manufacturer
sweetens the deal by offering to finance the purchase by lending you $100,000 for
five years, with annual interest payments of 5 percent. You would have to pay 13
percent to borrow from a bank. Your marginal tax rate is 35 percent ( ).
How much is this loan worth? If you take it, the cash flows, in thousands of dol-
lars, are
T
c
ϭ .35
Period
01 2 3 4 5
Cash flow 100
Tax shield
After-tax cash flow 100 Ϫ103.25Ϫ3.25Ϫ3.25Ϫ3.25Ϫ3.25
ϩ1.75ϩ1.75ϩ1.75ϩ1.75ϩ1.75

Ϫ105Ϫ5Ϫ5Ϫ5Ϫ5
What is the right discount rate?
Here you are discounting safe, nominal cash flows—safe because your company
must commit to pay if it takes the loan,
23
and nominal because the payments would
be fixed regardless of future inflation. Now, the correct discount rate for safe, nom-
inal cash flows is your company’s after-tax, unsubsidized borrowing rate.
24
In this
case r* ϭ r
D
11 Ϫ T
c
2ϭ .1311 Ϫ .352ϭ .0845. Therefore
23
In theory, safe means literally “risk-free,” like the cash returns on a Treasury bond. In practice, it means
that the risk of not paying or receiving a cash flow is small.
24
In Section 13.1 we calculated the NPV of subsidized financing using the pretax borrowing rate. Now you
can see that was a mistake. Using the pretax rate implicitly defines the loan in terms of its pretax cash flows,
violating a rule promulgated way back in Section 6.1: Always estimate cash flows on an after-tax basis.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill

Companies, 2003
The manufacturer has effectively cut the machine’s purchase price from $100,000
to . You can now go back and recalculate the ma-
chine’s NPV using this fire-sale price, or you can use the NPV of the subsidized
loan as one element of the machine’s adjusted present value.
A General Rule
Clearly, we owe an explanation of why is the right discount rate for safe,
nominal cash flows. It’s no surprise that the rate depends on , the unsubsidized
borrowing rate, for that is investors’ opportunity cost of capital, the rate they
would demand from your company’s debt. But why should be converted to an
after-tax figure?
Let’s simplify by taking a one-year subsidized loan of $100,000 at 5 percent. The
cash flows, in thousands of dollars, are
r
D
r
D
r
D
11 Ϫ T
c
2
$100,000 Ϫ $20,520 ϭ $79,480
ϭϩ20.52, or $20,520
NPV ϭϩ100 Ϫ
3.25
1.0845
Ϫ
3.25
11.08452

2
Ϫ
3.25
11.08452
3
Ϫ
3.25
11.08452
4
Ϫ
103.25
11.08452
5
CHAPTER 19 Financing and Valuation 545
Period 0 Period 1
Cash flow 100
Tax shield
After-tax cash flow 100 Ϫ103.25
ϩ1.75
Ϫ105
Now ask, What is the maximum amount X that could be borrowed for one year
through regular channels if $103,250 is set aside to service the loan?
“Regular channels” means borrowing at 13 percent pretax and 8.45 percent af-
ter tax. Therefore you will need 108.45 percent of the amount borrowed to pay back
principal plus after-tax interest charges. If , then .
Now if you can borrow $100,000 by a subsidized loan, but only $95,205 through
normal channels, the difference ($4,795) is money in the bank. Therefore, it must
also be the NPV of this one-period subsidized loan.
When you discount a safe, nominal cash flow at an after-tax borrowing rate, you
are implicitly calculating the equivalent loan, the amount you could borrow through

normal channels, using the cash flow as debt service. Note that
In some cases, it may be easier to think of taking the lender’s side of the equiva-
lent loan rather than the borrower’s. For example, you could ask, How much would
my company have to invest today in order to cover next year’s debt service on the
subsidized loan? The answer is $95,205: If you lend that amount at 13 percent, you
will earn 8.45 percent after tax, and therefore have . By
this transaction, you can in effect cancel, or “zero out,” the future obligation. If you
can borrow $100,000 and then set aside only $95,205 to cover all the required debt
service, you clearly have $4,795 to spend as you please. That amount is the NPV of
the subsidized loan.
95,20511.08452ϭ $103,250
Equivalent loan ϭ PV a
cash flow available
for debt service
bϭ
103,250
1.0845
ϭ 95,205
X ϭ 95,2051.0845X ϭ 103,250
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Therefore, regardless of whether it’s easier to think of borrowing or lending, the
correct discount rate for safe, nominal cash flows is an after-tax interest rate.

25
In some ways, this is an obvious result once you think about it. Companies are
free to borrow or lend money. If they lend, they receive the after-tax interest rate on
their investment; if they borrow in the capital market, they pay the after-tax inter-
est rate. Thus, the opportunity cost to companies of investing in debt-equivalent
cash flows is the after-tax interest rate. This is the adjusted cost of capital for debt-
equivalent cash flows.
26
Some Further Examples
Here are some further examples of debt-equivalent cash flows.
Payout Fixed by Contract Suppose you sign a maintenance contract with a truck
leasing firm, which agrees to keep your leased trucks in good working order for
the next two years in exchange for 24 fixed monthly payments. These payments are
debt-equivalent flows.
27
Depreciation Tax Shields Capital projects are normally valued by discounting
the total after-tax cash flows they are expected to generate. Depreciation tax shields
contribute to project cash flow, but they are not valued separately; they are just
folded into project cash flows along with dozens, or hundreds, of other specific in-
flows and outflows. The project’s opportunity cost of capital reflects the average
risk of the resulting aggregate.
However, suppose we ask what depreciation tax shields are worth by them-
selves. For a firm that’s sure to pay taxes, depreciation tax shields are a safe,
nominal flow. Therefore, they should be discounted at the firm’s after-tax bor-
rowing rate.
28
Suppose we buy an asset with a depreciable basis of $200,000, which can be de-
preciated by the five-year tax depreciation schedule (see Table 6.4). The resulting
tax shields are
546 PART V

Dividend Policy and Capital Structure
25
Borrowing and lending rates should not differ by much if the cash flows are truly safe, that is, if the
chance of default is small. Usually your decision will not hinge on the rate used. If it does, ask which
offsetting transaction—borrowing or lending—seems most natural and reasonable for the problem at
hand. Then use the corresponding interest rate.
26
All the examples in this section are forward-looking; they call for the value today of a stream of future
debt-equivalent cash flows. But similar issues arise in legal and contractual disputes when a past cash
flow has to be brought forward in time to a present value today. Suppose it’s determined that company
A should have paid B $1 million ten years ago. B clearly deserves more than $1 million today, because
it has lost the time value of money. The time value of money should be expressed as an after-tax bor-
rowing or lending rate, or if no risk enters, as the after-tax risk-free rate. The time value of money is not
equal to B’s overall cost of capital. Allowing B to “earn” its overall cost of capital on the payment allows
it to earn a risk premium without bearing risk. For a broader discussion of these issues, see F. Fisher and
C. Romaine, “Janis Joplin’s Yearbook and Theory of Damages,” Journal of Accounting, Auditing & Finance
5 (Winter/Spring 1990), pp. 145–157.
27
We assume you are locked into the contract. If it can be canceled without penalty, you may have a
valuable option.
28
The depreciation tax shields are cash inflows, not outflows as for the contractual payout or the subsi-
dized loan. For safe, nominal inflows, the relevant question is, How much could the firm borrow today
if it uses the inflow for debt service? You could also ask, How much would the firm have to lend today
to generate the same future inflow?